A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws
Year: 2014
Communications in Computational Physics, Vol. 16 (2014), Iss. 3 : pp. 718–763
Abstract
In this paper, we investigate the coupling of the Multi-dimensional Optimal Order Detection (MOOD) method and the Arbitrary high order DERivatives (ADER) approach in order to design a new high order accurate, robust and computationally efficient Finite Volume (FV) scheme dedicated to solving nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions, respectively. The Multi-dimensional Optimal Order Detection (MOOD) method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes. It is an arbitrary high-order accurate Finite Volume scheme in space, using polynomial reconstructions with a posteriori detection and polynomial degree decrementing processes to deal with shock waves and other discontinuities. In the following work, the time discretization is performed with an elegant and efficient one-step ADER procedure. Doing so, we retain the good properties of the MOOD scheme, that is to say, the optimal high-order of accuracy is reached on smooth solutions, while spurious oscillations near singularities are prevented. The ADER technique not only reduces the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D, but also increases the stability of the overall scheme. A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost, robustness, accuracy and efficiency. The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive (memory and/or CPU time), or because it is more accurate for a given grid resolution. A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws: the Euler equations of compressible gas dynamics, the classical equations of ideal magneto-Hydrodynamics (MHD) and finally the relativistic MHD equations (RMHD), which constitutes a particularly challenging nonlinear system of hyperbolic partial differential equation. All tests are run on genuinely unstructured grids composed of simplex elements.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.181113.140314a
Communications in Computational Physics, Vol. 16 (2014), Iss. 3 : pp. 718–763
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 46
-
A MOOD-MUSCL Hybrid Formulation for the Non-conservative Shallow-Water System
Figueiredo, J. | Clain, S.Journal of Scientific Computing, Vol. 88 (2021), Iss. 1
https://doi.org/10.1007/s10915-021-01513-z [Citations: 2] -
Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis
Zhao, Yong | Yu, Peng-Yao | Su, Shao-Juan | Wang, Tian-LinMathematical Problems in Engineering, Vol. 2018 (2018), Iss. P.1
https://doi.org/10.1155/2018/4859469 [Citations: 0] -
Shifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes
Ciallella, Mirco | Gaburro, Elena | Lorini, Marco | Ricchiuto, MarioApplied Mathematics and Computation, Vol. 441 (2023), Iss. P.127698
https://doi.org/10.1016/j.amc.2022.127698 [Citations: 1] -
Designing Several Types of Oscillation-Less and High-Resolution Hybrid Schemes on Block-Structured Grids
Jiang, Zhenhua | Yan, Chao | Yu, Jian | Lin, BoxiCommunications in Computational Physics, Vol. 21 (2017), Iss. 5 P.1376
https://doi.org/10.4208/cicp.OA-2015-0028 [Citations: 2] -
An efficient high order direct ALE ADER finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics
Boscheri, Walter
International Journal for Numerical Methods in Fluids, Vol. 84 (2017), Iss. 2 P.76
https://doi.org/10.1002/fld.4342 [Citations: 7] -
Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine
Dumbser, Michael | Fambri, Francesco | Tavelli, Maurizio | Bader, Michael | Weinzierl, TobiasAxioms, Vol. 7 (2018), Iss. 3 P.63
https://doi.org/10.3390/axioms7030063 [Citations: 41] -
An admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstruction
Blachère, F. | Turpault, R.Computer Methods in Applied Mechanics and Engineering, Vol. 317 (2017), Iss. P.836
https://doi.org/10.1016/j.cma.2017.01.012 [Citations: 12] -
High order direct Arbitrary-Lagrangian-Eulerian (ALE) PP schemes with WENO Adaptive-Order reconstruction on unstructured meshes
Boscheri, Walter | Balsara, Dinshaw S.Journal of Computational Physics, Vol. 398 (2019), Iss. P.108899
https://doi.org/10.1016/j.jcp.2019.108899 [Citations: 24] -
ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems
Reinarz, Anne | Charrier, Dominic E. | Bader, Michael | Bovard, Luke | Dumbser, Michael | Duru, Kenneth | Fambri, Francesco | Gabriel, Alice-Agnes | Gallard, Jean-Matthieu | Köppel, Sven | Krenz, Lukas | Rannabauer, Leonhard | Rezzolla, Luciano | Samfass, Philipp | Tavelli, Maurizio | Weinzierl, TobiasComputer Physics Communications, Vol. 254 (2020), Iss. P.107251
https://doi.org/10.1016/j.cpc.2020.107251 [Citations: 49] -
Space–time adaptive ADER-DG schemes for dissipative flows: Compressible Navier–Stokes and resistive MHD equations
Fambri, Francesco | Dumbser, Michael | Zanotti, OlindoComputer Physics Communications, Vol. 220 (2017), Iss. P.297
https://doi.org/10.1016/j.cpc.2017.08.001 [Citations: 48] -
Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables
Zanotti, Olindo | Dumbser, MichaelComputational Astrophysics and Cosmology, Vol. 3 (2016), Iss. 1
https://doi.org/10.1186/s40668-015-0014-x [Citations: 35] -
Three dimensional HLL Riemann solver for conservation laws on structured meshes; Application to Euler and magnetohydrodynamic flows
Balsara, Dinshaw S.
Journal of Computational Physics, Vol. 295 (2015), Iss. P.1
https://doi.org/10.1016/j.jcp.2015.03.056 [Citations: 50] -
Positivity preserving and entropy consistent approximate Riemann solvers dedicated to the high-order MOOD-based Finite Volume discretization of Lagrangian and Eulerian gas dynamics
Chan, Agnes | Gallice, Gérard | Loubère, Raphaël | Maire, Pierre-HenriComputers & Fluids, Vol. 229 (2021), Iss. P.105056
https://doi.org/10.1016/j.compfluid.2021.105056 [Citations: 14] -
A staggered semi-implicit hybrid FV/FE projection method for weakly compressible flows
Bermúdez, A. | Busto, S. | Dumbser, M. | Ferrín, J.L. | Saavedra, L. | Vázquez-Cendón, M.E.Journal of Computational Physics, Vol. 421 (2020), Iss. P.109743
https://doi.org/10.1016/j.jcp.2020.109743 [Citations: 42] -
A hybrid a posteriori MOOD limited lattice Boltzmann method to solve compressible fluid flows – LBMOOD
Kozhanova, Ksenia | Zhao, Song | Loubère, Raphaël | Boivin, PierreJournal of Computational Physics, Vol. 521 (2025), Iss. P.113570
https://doi.org/10.1016/j.jcp.2024.113570 [Citations: 0] -
Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data
Ciallella, Mirco | Clain, Stephane | Gaburro, Elena | Ricchiuto, MarioComputers & Mathematics with Applications, Vol. 175 (2024), Iss. P.1
https://doi.org/10.1016/j.camwa.2024.08.028 [Citations: 0] -
An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes
Escalante, C. | Dumbser, M. | Castro, M.J.Journal of Computational Physics, Vol. 394 (2019), Iss. P.385
https://doi.org/10.1016/j.jcp.2019.05.035 [Citations: 32] -
WENO schemes on unstructured meshes using a relaxed a posteriori MOOD limiting approach
Farmakis, Pericles S. | Tsoutsanis, Panagiotis | Nogueira, XesúsComputer Methods in Applied Mechanics and Engineering, Vol. 363 (2020), Iss. P.112921
https://doi.org/10.1016/j.cma.2020.112921 [Citations: 29] -
Adaptive-Mesh-Refinement for hyperbolic systems of conservation laws based on a posteriori stabilized high order polynomial reconstructions
Semplice, Matteo | Loubère, RaphaëlJournal of Computational Physics, Vol. 354 (2018), Iss. P.86
https://doi.org/10.1016/j.jcp.2017.10.031 [Citations: 8] -
A geometrically intrinsic lagrangian-Eulerian scheme for 2D shallow water equations with variable topography and discontinuous data
Abreu, Eduardo | Bachini, Elena | Pérez, John | Putti, MarioApplied Mathematics and Computation, Vol. 443 (2023), Iss. P.127776
https://doi.org/10.1016/j.amc.2022.127776 [Citations: 1] -
A posteriori limiting for 2D Lagrange plus Remap schemes solving the hydrodynamics system of equations
Braeunig, Jean-Philippe | Loubère, Raphaël | Motte, Renaud | Peybernes, Mathieu | Poncet, RaphaëlComputers & Fluids, Vol. 169 (2018), Iss. P.249
https://doi.org/10.1016/j.compfluid.2017.08.020 [Citations: 2] -
Hybrid finite volume weighted essentially non-oscillatory schemes with linear central reconstructions
Wang, Xiufang | Yu, Haiyan | Li, Gang | Gao, JinmeiApplied Mathematics and Computation, Vol. 359 (2019), Iss. P.132
https://doi.org/10.1016/j.amc.2019.04.025 [Citations: 1] -
A pressure-based semi-implicit space–time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier–Stokes equations at all Mach numbers
Tavelli, Maurizio | Dumbser, MichaelJournal of Computational Physics, Vol. 341 (2017), Iss. P.341
https://doi.org/10.1016/j.jcp.2017.03.030 [Citations: 91] -
High-accurate SPH method with Multidimensional Optimal Order Detection limiting
Nogueira, Xesús | Ramírez, Luis | Clain, Stéphane | Loubère, Raphaël | Cueto-Felgueroso, Luis | Colominas, IgnasiComputer Methods in Applied Mechanics and Engineering, Vol. 310 (2016), Iss. P.134
https://doi.org/10.1016/j.cma.2016.06.032 [Citations: 35] -
A posteriori sub-cell finite volume limiting of staggered semi-implicit discontinuous Galerkin schemes for the shallow water equations
Ioriatti, Matteo | Dumbser, MichaelApplied Numerical Mathematics, Vol. 135 (2019), Iss. P.443
https://doi.org/10.1016/j.apnum.2018.08.018 [Citations: 17] -
Comparison between a priori and a posteriori slope limiters for high-order finite volume schemes
Palafoutas, Jonathan | Velasco Romero, David A. | Teyssier, RomainJournal of Computational Physics, Vol. (2024), Iss. P.113571
https://doi.org/10.1016/j.jcp.2024.113571 [Citations: 0] -
Space–time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation
Popov, I.S.
Computers & Fluids, Vol. 284 (2024), Iss. P.106425
https://doi.org/10.1016/j.compfluid.2024.106425 [Citations: 0] -
Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations
Kuzmin, Dmitri | Klyushnev, NikitaJournal of Computational Physics, Vol. 407 (2020), Iss. P.109230
https://doi.org/10.1016/j.jcp.2020.109230 [Citations: 12] -
Direct Arbitrary-Lagrangian–Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws
Boscheri, Walter | Loubère, Raphaël | Dumbser, MichaelJournal of Computational Physics, Vol. 292 (2015), Iss. P.56
https://doi.org/10.1016/j.jcp.2015.03.015 [Citations: 55] -
Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems
A Conservative a-Posteriori Time-Limiting Procedure in Quinpi Schemes
Visconti, Giuseppe | Tozza, Silvia | Semplice, Matteo | Puppo, Gabriella2023
https://doi.org/10.1007/978-3-031-29875-2_9 [Citations: 0] -
Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows
Saurel, Richard | Pantano, CarlosAnnual Review of Fluid Mechanics, Vol. 50 (2018), Iss. 1 P.105
https://doi.org/10.1146/annurev-fluid-122316-050109 [Citations: 119] -
Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems
High-Order Arbitrary-Lagrangian-Eulerian Schemes on Crazy Moving Voronoi Meshes
Gaburro, Elena | Chiocchetti, Simone2023
https://doi.org/10.1007/978-3-031-29875-2_5 [Citations: 0] -
High order accurate conservative remapping scheme on polygonal meshes using a posteriori MOOD limiting
Blanchard, Ghislain | Loubère, RaphaëlComputers & Fluids, Vol. 136 (2016), Iss. P.83
https://doi.org/10.1016/j.compfluid.2016.06.002 [Citations: 21] -
Sharpening diffuse interfaces with compressible fluids on unstructured meshes
Chiapolino, Alexandre | Saurel, Richard | Nkonga, BonifaceJournal of Computational Physics, Vol. 340 (2017), Iss. P.389
https://doi.org/10.1016/j.jcp.2017.03.042 [Citations: 63] -
Efficient ROUND schemes on non-uniform grids applied to discontinuous Galerkin schemes with Godunov-type finite volume sub-cell limiting
Deng, Xi | Jiang, Zhen-hua | Yan, ChaoJournal of Computational Physics, Vol. 522 (2025), Iss. P.113575
https://doi.org/10.1016/j.jcp.2024.113575 [Citations: 0] -
Efficient methods with higher order interpolation and MOOD strategy for compressible turbulence simulations
Jiang, Zhen-Hua | Yan, Chao | Yu, JianJournal of Computational Physics, Vol. 371 (2018), Iss. P.528
https://doi.org/10.1016/j.jcp.2018.06.018 [Citations: 18] -
High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension
Chiocchetti, Simone | Peshkov, Ilya | Gavrilyuk, Sergey | Dumbser, MichaelJournal of Computational Physics, Vol. 426 (2021), Iss. P.109898
https://doi.org/10.1016/j.jcp.2020.109898 [Citations: 27] -
Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement
Zanotti, O. | Fambri, F. | Dumbser, M.Monthly Notices of the Royal Astronomical Society, Vol. 452 (2015), Iss. 3 P.3010
https://doi.org/10.1093/mnras/stv1510 [Citations: 70] -
High Order ADER Schemes for Continuum Mechanics
Busto, Saray | Chiocchetti, Simone | Dumbser, Michael | Gaburro, Elena | Peshkov, IlyaFrontiers in Physics, Vol. 8 (2020), Iss.
https://doi.org/10.3389/fphy.2020.00032 [Citations: 54] -
High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms
Boscheri, Walter | Loubère, RaphaëlCommunications in Computational Physics, Vol. 21 (2017), Iss. 1 P.271
https://doi.org/10.4208/cicp.OA-2015-0024 [Citations: 18] -
A high-order diffuse-interface method with TENO-THINC scheme for compressible multiphase flows
Li, Qichao | Lv, Yu | Fu, LinInternational Journal of Multiphase Flow, Vol. 173 (2024), Iss. P.104732
https://doi.org/10.1016/j.ijmultiphaseflow.2024.104732 [Citations: 3] -
Runge–Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics
Zhao, Jian | Tang, HuazhongJournal of Computational Physics, Vol. 343 (2017), Iss. P.33
https://doi.org/10.1016/j.jcp.2017.04.027 [Citations: 21] -
A filtering monotonization approach for DG discretizations of hyperbolic problems
Orlando, Giuseppe
Computers & Mathematics with Applications, Vol. 129 (2023), Iss. P.113
https://doi.org/10.1016/j.camwa.2022.11.017 [Citations: 3] -
A Priori Neural Networks Versus A Posteriori MOOD Loop: A High Accurate 1D FV Scheme Testing Bed
Bourriaud, Alexandre | Loubère, Raphaël | Turpault, RodolpheJournal of Scientific Computing, Vol. 84 (2020), Iss. 2
https://doi.org/10.1007/s10915-020-01282-1 [Citations: 5] -
An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows
Pantano, C. | Saurel, R. | Schmitt, T.Journal of Computational Physics, Vol. 335 (2017), Iss. P.780
https://doi.org/10.1016/j.jcp.2017.01.057 [Citations: 24] -
Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure
Tavelli, Maurizio | Chiocchetti, Simone | Romenski, Evgeniy | Gabriel, Alice-Agnes | Dumbser, MichaelJournal of Computational Physics, Vol. 422 (2020), Iss. P.109758
https://doi.org/10.1016/j.jcp.2020.109758 [Citations: 21] -
A strategy to implement Dirichlet boundary conditions in the context of ADER finite volume schemes. One-dimensional conservation laws
Montecinos, Gino I.
Computers & Fluids, Vol. 140 (2016), Iss. P.357
https://doi.org/10.1016/j.compfluid.2016.10.016 [Citations: 0] -
A Posteriori Subcell Finite Volume Limiter for General $$P_NP_M$$ Schemes: Applications from Gasdynamics to Relativistic Magnetohydrodynamics
Gaburro, Elena | Dumbser, MichaelJournal of Scientific Computing, Vol. 86 (2021), Iss. 3
https://doi.org/10.1007/s10915-020-01405-8 [Citations: 19] -
A Unified Framework for the Solution of Hyperbolic PDE Systems Using High Order Direct Arbitrary-Lagrangian–Eulerian Schemes on Moving Unstructured Meshes with Topology Change
Gaburro, Elena
Archives of Computational Methods in Engineering, Vol. 28 (2021), Iss. 3 P.1249
https://doi.org/10.1007/s11831-020-09411-7 [Citations: 21] -
The MOOD method for the non-conservative shallow-water system
Clain, S. | Figueiredo, J.Computers & Fluids, Vol. 145 (2017), Iss. P.99
https://doi.org/10.1016/j.compfluid.2016.11.013 [Citations: 16] -
Advancement of Shock Capturing Computational Fluid Dynamics Methods
Reconstruction and Slope Limiters
Kitamura, Keiichi
2020
https://doi.org/10.1007/978-981-15-9011-5_5 [Citations: 0] -
An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes
Boscheri, W. | Dumbser, M.Journal of Scientific Computing, Vol. 66 (2016), Iss. 1 P.240
https://doi.org/10.1007/s10915-015-0019-2 [Citations: 15] -
Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms
Turpault, Rodolphe
Numerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 6
https://doi.org/10.1002/num.23118 [Citations: 0] -
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
Peshkov, Ilya | Boscheri, Walter | Loubère, Raphaël | Romenski, Evgeniy | Dumbser, MichaelJournal of Computational Physics, Vol. 387 (2019), Iss. P.481
https://doi.org/10.1016/j.jcp.2019.02.039 [Citations: 37] -
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
Dumbser, Michael | Zanotti, Olindo | Loubère, Raphaël | Diot, StevenJournal of Computational Physics, Vol. 278 (2014), Iss. P.47
https://doi.org/10.1016/j.jcp.2014.08.009 [Citations: 258] -
Cell centered direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes for nonlinear hyperelasticity
Boscheri, Walter | Dumbser, Michael | Loubère, RaphaëlComputers & Fluids, Vol. 134-135 (2016), Iss. P.111
https://doi.org/10.1016/j.compfluid.2016.05.004 [Citations: 32] -
A single-step third-order temporal discretization with Jacobian-free and Hessian-free formulations for finite difference methods
Lee, Youngjun | Lee, DongwookJournal of Computational Physics, Vol. 427 (2021), Iss. P.110063
https://doi.org/10.1016/j.jcp.2020.110063 [Citations: 4] -
High Order Direct Arbitrary-Lagrangian–Eulerian (ALE) Finite Volume Schemes for Hyperbolic Systems on Unstructured Meshes
Boscheri, Walter
Archives of Computational Methods in Engineering, Vol. 24 (2017), Iss. 4 P.751
https://doi.org/10.1007/s11831-016-9188-x [Citations: 15] -
High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids
Dumbser, Michael | Peshkov, Ilya | Romenski, Evgeniy | Zanotti, OlindoJournal of Computational Physics, Vol. 314 (2016), Iss. P.824
https://doi.org/10.1016/j.jcp.2016.02.015 [Citations: 138] -
Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws
Toro, Eleuterio F. | Montecinos, Gino I.Journal of Computational Physics, Vol. 303 (2015), Iss. P.146
https://doi.org/10.1016/j.jcp.2015.09.039 [Citations: 25] -
Hybrid central-upwind finite volume schemes for solving the Euler and Navier–Stokes equations
Jiang, Zhen-Hua | Yan, Chao | Yu, Jian | Li, YansuComputers & Mathematics with Applications, Vol. 72 (2016), Iss. 9 P.2241
https://doi.org/10.1016/j.camwa.2016.08.022 [Citations: 5] -
An ADER-type scheme for a class of equations arising from the water-wave theory
Montecinos, G.I. | López-Rios, J.C. | Lecaros, R. | Ortega, J.H. | Toro, E.F.Computers & Fluids, Vol. 132 (2016), Iss. P.76
https://doi.org/10.1016/j.compfluid.2016.04.012 [Citations: 5] -
A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics
Boscheri, Walter | Dumbser, Michael | Loubère, Raphaël | Maire, Pierre-HenriJournal of Computational Physics, Vol. 358 (2018), Iss. P.103
https://doi.org/10.1016/j.jcp.2017.12.040 [Citations: 23] -
a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations
Clain, Stéphane | Loubère, Raphaël | Machado, Gaspar J.Advances in Computational Mathematics, Vol. 44 (2018), Iss. 2 P.571
https://doi.org/10.1007/s10444-017-9556-6 [Citations: 7] -
A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes
Dumbser, Michael | Loubère, RaphaëlJournal of Computational Physics, Vol. 319 (2016), Iss. P.163
https://doi.org/10.1016/j.jcp.2016.05.002 [Citations: 100] -
Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes
Gaburro, Elena | Dumbser, Michael | Castro, Manuel J.Computers & Fluids, Vol. 159 (2017), Iss. P.254
https://doi.org/10.1016/j.compfluid.2017.09.022 [Citations: 33] -
Advanced Topics in Nonsmooth Dynamics
Nonsmooth Modal Analysis: From the Discrete to the Continuous Settings
Thorin, Anders | Legrand, Mathias2018
https://doi.org/10.1007/978-3-319-75972-2_5 [Citations: 3] -
A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model
Kemm, Friedemann | Gaburro, Elena | Thein, Ferdinand | Dumbser, MichaelComputers & Fluids, Vol. 204 (2020), Iss. P.104536
https://doi.org/10.1016/j.compfluid.2020.104536 [Citations: 36] -
Simple a posteriori slope limiter (Post Limiter) for high resolution and efficient flow computations
Kitamura, Keiichi | Hashimoto, AtsushiJournal of Computational Physics, Vol. 341 (2017), Iss. P.313
https://doi.org/10.1016/j.jcp.2017.04.002 [Citations: 11] -
A higher‐order unsplit 2D direct Eulerian finite volume method for two‐material compressible flows based on the MOOD paradigms
Diot, S. | François, M. M. | Dendy, E. D.International Journal for Numerical Methods in Fluids, Vol. 76 (2014), Iss. 12 P.1064
https://doi.org/10.1002/fld.3966 [Citations: 2] -
Solution property preserving reconstruction for finite volume scheme: a boundary variation diminishing+multidimensional optimal order detection framework
Tann, Siengdy | Deng, Xi | Shimizu, Yuya | Loubère, Raphaël | Xiao, FengInternational Journal for Numerical Methods in Fluids, Vol. 92 (2020), Iss. 6 P.603
https://doi.org/10.1002/fld.4798 [Citations: 11] -
High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes
Boscheri, Walter | Dumbser, Michael | Zanotti, OlindoJournal of Computational Physics, Vol. 291 (2015), Iss. P.120
https://doi.org/10.1016/j.jcp.2015.02.052 [Citations: 26] -
A Staggered Semi-implicit Discontinuous Galerkin Scheme with a Posteriori Subcell Finite Volume Limiter for the Euler Equations of Gasdynamics
Ioriatti, Matteo | Dumbser, Michael | Loubère, RaphaëlJournal of Scientific Computing, Vol. 83 (2020), Iss. 2
https://doi.org/10.1007/s10915-020-01209-w [Citations: 3] -
Discontinuous Galerkin Methods for Compressible and Incompressible Flows on Space–Time Adaptive Meshes: Toward a Novel Family of Efficient Numerical Methods for Fluid Dynamics
Fambri, Francesco
Archives of Computational Methods in Engineering, Vol. 27 (2020), Iss. 1 P.199
https://doi.org/10.1007/s11831-018-09308-6 [Citations: 13] -
A direct Arbitrary-Lagrangian–Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D
Boscheri, Walter | Dumbser, MichaelJournal of Computational Physics, Vol. 275 (2014), Iss. P.484
https://doi.org/10.1016/j.jcp.2014.06.059 [Citations: 106] -
High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
Gaburro, Elena | Boscheri, Walter | Chiocchetti, Simone | Klingenberg, Christian | Springel, Volker | Dumbser, MichaelJournal of Computational Physics, Vol. 407 (2020), Iss. P.109167
https://doi.org/10.1016/j.jcp.2019.109167 [Citations: 72] -
A MOOD-like compact high order finite volume scheme with adaptive mesh refinement
Loubère, Raphaël | Turpault, Rodolphe | Bourriaud, AlexandreApplied Mathematics and Computation, Vol. 443 (2023), Iss. P.127792
https://doi.org/10.1016/j.amc.2022.127792 [Citations: 1] -
Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
Zanotti, Olindo | Fambri, Francesco | Dumbser, Michael | Hidalgo, ArturoComputers & Fluids, Vol. 118 (2015), Iss. P.204
https://doi.org/10.1016/j.compfluid.2015.06.020 [Citations: 118] -
A relaxed a posteriori MOOD algorithm for multicomponent compressible flows using high-order finite-volume methods on unstructured meshes
Tsoutsanis, Panagiotis | Pavan Kumar, Machavolu Sai Santosh | Farmakis, Pericles S.Applied Mathematics and Computation, Vol. 437 (2023), Iss. P.127544
https://doi.org/10.1016/j.amc.2022.127544 [Citations: 2] -
A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism
Balsara, Dinshaw S. | Amano, Takanobu | Garain, Sudip | Kim, JinhoJournal of Computational Physics, Vol. 318 (2016), Iss. P.169
https://doi.org/10.1016/j.jcp.2016.05.006 [Citations: 43] -
A triangle-based positive semi-discrete Lagrangian–Eulerian scheme via the weak asymptotic method for scalar equations and systems of hyperbolic conservation laws
Abreu, Eduardo | Agudelo, Jorge | Pérez, JohnJournal of Computational and Applied Mathematics, Vol. 437 (2024), Iss. P.115465
https://doi.org/10.1016/j.cam.2023.115465 [Citations: 0] -
Reprint of: Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes
Gaburro, Elena | Dumbser, Michael | Castro, Manuel J.Computers & Fluids, Vol. 169 (2018), Iss. P.263
https://doi.org/10.1016/j.compfluid.2018.03.051 [Citations: 3] -
Space-Time Adaptive ADER-DG Finite Element Method with LST-DG Predictor and a posteriori Sub-cell WENO Finite-Volume Limiting for Simulation of Non-stationary Compressible Multicomponent Reactive Flows
Popov, I. S.
Journal of Scientific Computing, Vol. 95 (2023), Iss. 2
https://doi.org/10.1007/s10915-023-02164-y [Citations: 4] -
Efficient implementation of space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows
Popov, Ivan S
Journal of Physics: Conference Series, Vol. 1740 (2021), Iss. 1 P.012059
https://doi.org/10.1088/1742-6596/1740/1/012059 [Citations: 0] -
High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation
Bergmann, Michel | Bouharguane, Afaf | Iollo, Angelo | Tardieu, AlexisCommunications on Applied Mathematics and Computation, Vol. 6 (2024), Iss. 3 P.1954
https://doi.org/10.1007/s42967-023-00355-w [Citations: 0] -
Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers
Balsara, Dinshaw S. | Dumbser, MichaelJournal of Computational Physics, Vol. 299 (2015), Iss. P.687
https://doi.org/10.1016/j.jcp.2015.07.012 [Citations: 81] -
An almost fail-safe a-posteriori limited high-order CAT scheme
Macca, Emanuele | Loubère, Raphaël | Parés, Carlos | Russo, GiovanniJournal of Computational Physics, Vol. 498 (2024), Iss. P.112650
https://doi.org/10.1016/j.jcp.2023.112650 [Citations: 3]